I'm not sure if they're suggesting that for any complex number w, a function f with an essential singularity at has the property that as z . This seems intuitively to just be not true at all, but to be fair, the book's description of essential singularities is "we leave essential singularities to the exercises."

I'm not sure if they're suggesting that for any complex number w, a function f with an essential singularity at has the property that as z . This seems intuitively to just be not true at all, but to be fair, the book's description of essential singularities is "we leave essential singularities to the exercises."

Well, which definition did they give you in the exercises. That it's a singularity which is neither removable or a pole or that neither or exists?

Mar 12th 2010, 05:11 PM

davismj

Quote:

Originally Posted by Drexel28

Well, which definition did they give you in the exercises. That it's a singularity which is neither removable or a pole or that neither or exists?

Neither pole nor removable.

They also give the hint: if g is bounded, then show that f has a pole or a removable singularity at . This implies that as ?